of \mathbb{R}^3:
(a) Find the coordinate vector of $x = \begin{bmatrix} -1 \ -3 \ 5 \end{bmatrix}$ with respect to the ordered basis
$E = \left\{ \begin{bmatrix} 1 \ 6 \ 7 \end{bmatrix}, \begin{bmatrix} 0 \ 1 \ -2 \end{bmatrix}, \begin{bmatrix} 0 \ 0 \ 1 \end{bmatrix} \right\}$
$[x]_E = \begin{bmatrix} \\\\\\ \end{bmatrix}$
(b) Let $F_1$ be the ordered basis of $\mathbb{R}^2$ given by
$F_1 = \left\{ \begin{bmatrix} 4 \ -2 \end{bmatrix}, \begin{bmatrix} 1 \ 5 \end{bmatrix} \right\}$
and let $F_2$ be the ordered basis given by
$F_2 = \left\{ \begin{bmatrix} 2 \ 1 \end{bmatrix}, \begin{bmatrix} 3 \ 2 \end{bmatrix} \right\}$
Find the transition matrix $P_{F_2 \leftarrow F_1}$ such that $[x]_{F_2} = P_{F_2 \leftarrow F_1} [x]_{F_1}$ for all $x$ in $\mathbb{R}^2$:
$P = \begin{bmatrix} \\\\\\ \end{bmatrix}$
